{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T01:26:37Z","timestamp":1773883597937,"version":"3.50.1"},"reference-count":60,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,12,16]]},"abstract":"<jats:p>Aggregation of q-rung orthopair fuzzy information serves as an important branch of the q-rung orthopair fuzzy set theory, where operations on q-rung orthopair fuzzy values (q-ROFVs) play a crucial role. Recently, aggregation operators on q-ROFVs were established by employing the Einstein operations rather than the algebraic operations. In this paper, we give a further investigation on operations and aggregation operators for q-ROFVs based on the Einstein operational laws. We present the operational principles of Einstein operations over q-ROFVs and compare them with those built on the algebraic operations. The properties of the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator and q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator are investigated in detail, such as idempotency, monotonicity, boundedness, shift-invariance and homogeneity. Then, the developed operators are applied to multiattribute decision making problems under the q-rung orthopair fuzzy environment. Finally, an example for selecting the design scheme for a blockchain-based agricultural product traceability system is presented to illustrate the feasibility and effectiveness of the proposed methods.<\/jats:p>","DOI":"10.3233\/jifs-210548","type":"journal-article","created":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T16:38:34Z","timestamp":1632847114000},"page":"6655-6673","source":"Crossref","is-referenced-by-count":9,"title":["A further investigation on q-rung orthopair fuzzy Einstein aggregation operators"],"prefix":"10.1177","volume":"41","author":[{"given":"Wen Sheng","family":"Du","sequence":"first","affiliation":[{"name":"School of Business, Zhengzhou University, Zhengzhou, P.R. 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